Compressive spectral image super-resolution by using singular value decomposition

Marquez, Miguel; Mejia, Yuri; Argüello, Henry

doi:10.1016/j.optcom.2017.06.079

Cited by 11 publications

(5 citation statements)

References 19 publications

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“…The comparison methods are Cholesky decomposition, 8 QR factorization, 9 and the block-diagonal (BD) method 11 . The Cholesky decomposition and QR factorization decompose H into boldLL* and QR, respectively.…”

Section: Experiments and Resultsmentioning

confidence: 99%

“…There are several standard methods to efficiently compute this inverse, such as the Cholesky decomposition, 8 the QR factorization, 9,10 and the block-diagonal (BD) method. 11 The Cholesky decomposition asserts that a real Hermitian and positive definite matrix A can be expressed as A ¼ LL T , where L represents a lower triangular matrix with strictly positive diagonal entries and L T denotes its transpose. The desired inversion can then be computed as…”

Section: Introductionmentioning

confidence: 99%

“…It is precisely this operation that appears as one of the proximal operators needed to execute the ADMM algorithm on a CASSI system. There are several standard methods to efficiently compute this inverse, such as the Cholesky decomposition, 8 the QR factorization, 9 , 10 and the block-diagonal (BD) method 11 …”

Section: Introductionmentioning

confidence: 99%

“…The comparison methods are Cholesky decomposition, 8 QR factorization, 9 and the blockdiagonal (BD) method. 11 The Cholesky decomposition and QR factorization decompose H into LL Ã and QR, respectively. Each of these matrices has specific properties that enable the efficient computation of the inverse matrices.…”

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confidence: 99%

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Fast matrix inversion in compressive spectral imaging based on a tensorial representation

Carlsson,

Martinez,

Vargas

et al. 2024

J. Electron. Imag.

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Snapshot spectral imaging enables the acquisition of hyperspectral images (HSI) employing specialized optical systems, such as the coded aperture snapshot spectral imager (CASSI). Specifically, the CASSI system performs spatiospectral codification of light obtaining two-dimensional projected measurements, and these measurements are then processed by computational algorithms to obtain the desired spectral images. However, because HSIs often have a high spatial or spectral resolution, the sensing matrix related to the acquisition protocol becomes very large, leading to a high computational storage cost and long computation times. In this work, we propose an algebraic framework for computing the relevant operations in a tensorial form based on the nature of the codification protocol. We then test our framework against some comparison methods based on linear algebra decomposition, factorization, or block-operations, demonstrating that the proposed method is between 3 and 20 times faster than the best-competing method. Moreover, the gain becomes larger when the matrices become bigger, corresponding to realistic HSI sizes for spectral imaging applications. In extreme cases, our method can still operate when the competing methods stall due to memory shortage.

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Section: Experiments and Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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Fast matrix inversion in compressive spectral imaging based on a tensorial representation

Carlsson,

Martinez,

Vargas

et al. 2024

J. Electron. Imag.

Self Cite

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“…To overcome these challenges, recent approaches have The work of Jonathan Monsalve is supported by a Colciencias/Santander department Scholarship (771 of 2016) explored the use of Compressive Spectral Imaging (CSI) theory [6,7]. Because CSI imagers acquire a compressed version of the spectral image [8,9,10], conventional CM estimators require the reconstruction of the signal. To avoid this costly reconstruction step, Compressive Covariance Sampling (CCS) has emerged as an alternative to estimate the covariance matrix directly from the compressive measurements.…”

Section: Introductionmentioning

confidence: 99%

Compressive Covariance Matrix Estimation from a Dual-Dispersive Coded Aperture Spectral Imager

Monsalve

Marquez

Esnaola

et al. 2021

2021 IEEE International Conference on Image Processing (ICIP)

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Compressive covariance sampling (CCS) theory aims to recover the covariance matrix (CM) of a signal, instead of the signal itself, from a reduced set of random linear projections. Although several theoretical works demonstrate the CCS theory's advantages in compressive spectral imaging tasks, a real optical implementation has no been proposed. Therefore, this paper proposes a compressive spectral sensing protocol for the dual-dispersive coded aperture spectral snapshot imager (DD-CASSI) to directly estimate the covariance matrix of the signal. Specifically, we propose a coded aperture design that allows recasting the vector sensing problem into matrix form, which enables to exploit the covariance matrix structure such as positive-semidefiniteness, low-rank, or Toeplitz. Additionally, a low-rank approximation of the image is reconstructed using a Principal Components Analysis (PCA) based method. In order to test the precision of the reconstruction, some spectral signatures of the image are captured with a spectrometer and compared with those obtained in the reconstruction using the covariance matrix. Results show the reconstructed spectrum is accurate with a spectral angle mapper (SAM) of less than 14 o . RGB image composites of the spectral image also provide evidence of a correct color reconstruction.

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Wind field reconstruction using dimension-reduction of CFD data with experimental validation

Qin

Shi

et al. 2018

Energy

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Compressive spectral image super-resolution by using singular value decomposition

Cited by 11 publications

References 19 publications

Fast matrix inversion in compressive spectral imaging based on a tensorial representation

Fast matrix inversion in compressive spectral imaging based on a tensorial representation

Compressive Covariance Matrix Estimation from a Dual-Dispersive Coded Aperture Spectral Imager

Wind field reconstruction using dimension-reduction of CFD data with experimental validation

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